Elementary properties of groups and rings, including symmetric groups, properties of the integers, polynomial rings, elementary field theory. Three lecture hours a week for one semester. Students who have received a grade of C- or better in Mathematics 373K may not take Mathematics 343K. Prerequisite: Mathematics 325K, 333L, or Philosophy 313K, and Mathematics 328K or 341 with a grade of at least C- in each; or consent of the undergraduate advisor.